A bowling ball sits on a hard floor at a point which we take to be the origin. T

Question

A bowling ball sits on a hard floor at a point which we take to be the origin. The ball is hit some number of times by a hammer. The ball moves along a line back and forth across the floor as a result of the hits. The region to the right of the origin is taken to be positive, but during its motion the ball is at times on both sides of the origin. After the ball has been moving for a while, a sonic ranger is started and takes the following graph of the ball's velocity.

Answer the following questions with the symbols L (left), R (right), N (neither), or C (cannot say which). Each question only refers to the time interval displayed by the computer.

A. Which side of the origin is the ball at for the time marked A?

B. At the time marked B, in which direction is the ball moving?

C. Between the times A and C, what is the direction of the ball's displacement?

D. The ball receives a hit at the time marked D. What is the direction the ball is moving after that hit?

E. What is the direction of the ball's average acceleration around the time marked D, due to the hit?

F. What direction is the net force on the ball around the time marked D, due to the hit?

G. What direction is the net force on the ball at the time marked B?

Explanation / Answer

A:- C.

At time A, the ball could be at any side of the origin but its velocity is positive.

B:- L.

Before time B, the velocity time graph cut the x axis indicating that when the ball was moving with postive velocity, it decelerated to zero velocity at the instant of crossing the x axis and then started accelerating towards left for some time and then its velocity became constant in the negative direction. This means the ball is now moving towards left.

C:- R.

Evidently, from the graph, area under the v-t graph is positive which means the displacement is positive. As right side of the origin is considered positive, displacement is towards the right.

D:- R.

The ball was moving rightwards before being hit and continues to move rightwards as velocity is still positive. But after D, it attains a constant velocity for sometime unlike a few moments before D when it was decelerating.

E:- L.

RIght before D, the ball was decelerating (evident from the negative slope of the graph) but it still continues to move rightward. But its acceleration is leftward (as it is negative) and hence retards the ball to a slightly lesser velocity.

F:- L.

It follows from the previous part that the acceleration is towards the left because it is negative. As the net force here is only due to the hits, the force is also in the leftward direction (force being the product of mass and acceleration and acceleration being the only vector deciding the direction of motion).

G:- N.

At B, the ball has no acceleration and hence, no force. Thus, the force is in neither direction.

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